Results 91 to 100 of about 82,476 (235)
Spectral Theory of the Riemann Zeta-Function: Chapter 6: Appendix [PDF]
arXiv, 2008 The main aim of this article is to develop, in a fully detailed fashion, a {\bf unified} theory of the spectral theory of mean values of individual automorphic L-functions which is a natural extension of the fourth moment of the Riemann zeta-function but does not admit any analogous argument and requires a genuinely new method.
arxiv
Notes on the Riemann zeta-function-IV [PDF]
Hardy-Ramanujan Journal, 1999 In earlier papers of this series III and IV, poles of certain meromorphic functions involving Riemann's zeta-function at shifted arguments and Dirichlet polynomials were studied. The functions in question were quotients of products of such functions, and it was shown that they have ``many'' poles.
K. Srinivas +3 more
openaire +4 more sources
A short proof of Helson's conjecture
Bulletin of the London Mathematical Society, Volume 57, Issue 4, Page 1065-1076, April 2025.Abstract Let α:N→S1$\alpha \colon \mathbb {N}\rightarrow S^1$ be the Steinhaus multiplicative function: a completely multiplicative function such that (α(p))pprime$(\alpha (p))_{p\text{ prime}}$ are i.i.d. random variables uniformly distributed on the complex unit circle S1$S^1$. Helson conjectured that E|∑n⩽xα(n)|=o(x)$\mathbb {E}|\sum _{n\leqslant x}\
Ofir Gorodetsky, Mo Dick Wong
wiley +1 more source
Joint universality of some zeta-functions. I
Lietuvos Matematikos Rinkinys, 2010 In the paper, the joint universality for the Riemann zeta-function and a collection of periodic Hurwitz zeta functions is discussed and basic results are given.
Santa Račkauskienė +1 more
doaj +1 more source
Riemann zeros from Floquet engineering a trapped-ion qubit
npj Quantum Information, 2021 The non-trivial zeros of the Riemann zeta function are central objects in number theory. In particular, they enable one to reproduce the prime numbers. They have also attracted the attention of physicists working in random matrix theory and quantum chaos
Ran He +8 more
doaj +1 more source
Riemann-Roch for Toric Rank Functions [PDF]
arXiv, 2022 In this thesis we study toric rank functions for chip firing games and prove special cases of a conjectural Riemann-Roch. The original motivation for an investigation into this area of study came for the adaptation (due to Matt Baker) of Riemann-Roch into a graph theoretic analogue through the use of chip-firing games.
arxiv
Fractional derivative of the riemann zeta function
, 2017 Fractional derivative of the Riemann zeta ...
E. Guariglia
semanticscholar +1 more source
Riemann-Roch and Riemann-Hurwitz theorems for global fields [PDF]
arXiv, 2009 In this paper, we use counting theorems from the geometry of numbers to extend the Riemann-Roch theorem and the Riemann-Hurwitz formula to global fields of arbitrary characteristic.
arxiv
On Artin's conjecture on average and short character sums
Bulletin of the London Mathematical Society, EarlyView.Abstract Let Na(x)$N_a(x)$ denote the number of primes up to x$x$ for which the integer a$a$ is a primitive root. We show that Na(x)$N_a(x)$ satisfies the asymptotic predicted by Artin's conjecture for almost all 1⩽a⩽exp((loglogx)2)$1\leqslant a\leqslant \exp ((\log \log x)^2)$. This improves on a result of Stephens (1969).
Oleksiy Klurman +2 more
wiley +1 more source
Mathematical Methods in the Applied Sciences, Volume 48, Issue 9, Page 9920-9933, June 2025.ABSTRACT In this article, we provided fixed‐point results for (Θ,G1)$$ \left(\Theta, {G}_1\right) $$‐quasirational contraction and (Θ,G2)$$ \left(\Theta, {G}_2\right) $$‐quasirational contraction within the setting of triple controlled metric‐like spaces.
Sadia Farooq +3 more
wiley +1 more source